The endpoint theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It plays a fundamental role in the theory of the abstract boundary as it implies that there is always an abstract boundary point to represent the endpoint of such sequences and curves. The endpoint theorem will be of interest to researchers analysing specific spacetimes as it shows how to construct a chart in the original manifold which contains the sequence (curve). In particular, it has application to the study of singularities predicted by the singularity theorems.

端点定理将流形中没有累积点的序列（曲线）的存在与该流形的开放嵌入的存在联系起来，因此给定序列（曲线）的图像具有唯一的端点。它在抽象边界理论中起着基础性的作用，因为它暗示总是有一个抽象边界点来表示这些序列和曲线的端点。端点定理将引起分析特定时空的研究人员的兴趣，因为它显示了如何在包含序列（曲线）的原始流形中构建图表。特别是，它适用于奇点定理预测的奇点研究。